# 6TH GR. ALGEBRA

posted by Amelia

EXTENDING THE LESSON If you add any two rational numbers, the sum is always a rational number. So, the set of rational numbers is closed under addition. Is the set of rational numbers closed under subtraction. multiplication,and division also? Explain.

1. Marth

Can you think of any two numbers that, when subtracted, multiplied, or divided, yield a number that is not rational? For example, take the rational numbers 2 and 3.

2 - 3 = -1
2 * 3 = 6
2 / 3 = 2/3

Are any of the results irrational? And are there any other rational numbers that yield different results?

(I assume a formal proof is not requested).

2. Amelia

Can you think of any two numbers that, when subtracted, multiplied, or divided, yield a number that is not rational? For example, take the rational numbers 2 and 3.

2 - 3 = -1
2 * 3 = 6
2 / 3 = 2/3

Are any of the results irrational? And are there any other rational numbers that yield different results?

yes this one 2 * 3 = 6

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